Correlation Coefficient

Front

What is the correlation coefficient (r)?

Back

The correlation coefficient (r) is a statistical measure that describes the strength and direction of a relationship between two variables, ranging from -1 to 1.

Front

What does a correlation coefficient of r = 0.89 indicate?

Back

A correlation coefficient of r = 0.89 indicates a strong positive linear relationship between the two variables.

Front

What is the coefficient of determination (R²)?

Back

The coefficient of determination (R²) is the proportion of the variance in the dependent variable that is predictable from the independent variable, calculated as the square of the correlation coefficient.

Front

If the coefficient of determination is 0.72, what percentage of the variation is explained?

Back

72% of the variation in the dependent variable is explained by the independent variable.

Front

How do you calculate the coefficient of determination from the correlation coefficient?

Back

The coefficient of determination (R²) is calculated by squaring the correlation coefficient (r). For example, if r = 0.865, then R² = 0.865² = 0.748.

Front

What does a coefficient of determination of 0.748 mean?

Back

A coefficient of determination of 0.748 means that approximately 74.8% of the variance in the dependent variable can be explained by the independent variable.

Front

What does the coefficient of determination tell us about the data?

Back

The coefficient of determination tells us the percentage of data that is on the line of best fit, indicating how well the model explains the data.

Front

What is the relationship between time taken to get to school and distance travelled?

Back

There is an expected positive association; as the distance travelled increases, the time taken to get to school is likely to increase.

Front

What does a negative correlation coefficient indicate?

Back

A negative correlation coefficient indicates an inverse relationship between two variables; as one variable increases, the other decreases.

Front

What is the range of values for the correlation coefficient?

Back

The correlation coefficient ranges from -1 to 1.